Research on children's online experience and computer interaction often overlooks the relationship children have with hidden algorithms that control the content they encounter. Furthermore, it is not only about how children interact with targeted content but also how their development and agency are largely affected by these. By engaging with the body of literature at the intersection of i) human-centered design approaches, ii) exclusion and discrimination in A.I., iii) privacy, transparency, and accountability, and iv) children's online citizenship, this article dives into the question of "How can we approach the design of a child-centered moderation process to (1) include aspects that families value for their children and (2) provide explanations for content appropriateness and removal so that we can scale (according to systems and human needs) the moderation process assisted by A.I.?". This article contributes a sociotechnical highlight of core challenges and opportunities of designing child-centered content control tools. The article concludes by grounding and characterizing design considerations for a child-centered, family-guided moderation system. We hope this work serves as a stepping stone for designers and researchers pursuing children's safety online with an eye on hidden agents controlling children's online experiences and, by extension, the values and opportunities children are exposed to.